Average Error: 0.2 → 0.2
Time: 8.6s
Precision: binary64
Cost: 704
\[\left(0 < m \land 0 < v\right) \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
↓
\[m \cdot \left(\frac{m}{v} \cdot \left(1 - m\right) + -1\right) \]
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v) :precision binary64 (* m (+ (* (/ m v) (- 1.0 m)) -1.0)))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * m;
}
↓
double code(double m, double v) {
	return m * (((m / v) * (1.0 - m)) + -1.0);
}

real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    code = (((m * (1.0d0 - m)) / v) - 1.0d0) * m
end function
↓
real(8) function code(m, v)
    real(8), intent (in) :: m
    real(8), intent (in) :: v
    code = m * (((m / v) * (1.0d0 - m)) + (-1.0d0))
end function

public static double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * m;
}
↓
public static double code(double m, double v) {
	return m * (((m / v) * (1.0 - m)) + -1.0);
}

def code(m, v):
	return (((m * (1.0 - m)) / v) - 1.0) * m
↓
def code(m, v):
	return m * (((m / v) * (1.0 - m)) + -1.0)

function code(m, v)
	return Float64(Float64(Float64(Float64(m * Float64(1.0 - m)) / v) - 1.0) * m)
end
↓
function code(m, v)
	return Float64(m * Float64(Float64(Float64(m / v) * Float64(1.0 - m)) + -1.0))
end

function tmp = code(m, v)
	tmp = (((m * (1.0 - m)) / v) - 1.0) * m;
end
↓
function tmp = code(m, v)
	tmp = m * (((m / v) * (1.0 - m)) + -1.0);
end

code[m_, v_] := N[(N[(N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision] - 1.0), $MachinePrecision] * m), $MachinePrecision]
↓
code[m_, v_] := N[(m * N[(N[(N[(m / v), $MachinePrecision] * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]

\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\frac{m}{v} \cdot \left(1 - m\right) + -1\right)

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]

  2. Simplified0.2

    \[\leadsto \color{blue}{m \cdot \left(\frac{m}{v} \cdot \left(1 - m\right) + -1\right)} \]
    Proof
    (*.f64 m (+.f64 (*.f64 (/.f64 m v) (-.f64 1 m)) -1)): 0 points increase in error, 0 points decrease in error
    (*.f64 m (+.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 m (-.f64 1 m)) v)) -1)): 10 points increase in error, 1 points decrease in error
    (*.f64 m (+.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)) -1)): 0 points increase in error, 0 points decrease in error
    (*.f64 m (+.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (*.f64 m (-.f64 1 m)) 1) v)) -1)): 0 points increase in error, 0 points decrease in error
    (*.f64 m (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v))) -1)): 23 points increase in error, 9 points decrease in error
    (*.f64 m (+.f64 (*.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) (Rewrite<= metadata-eval (neg.f64 1)))): 0 points increase in error, 0 points decrease in error
    (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) m) (*.f64 (neg.f64 1) m))): 2 points increase in error, 2 points decrease in error
    (+.f64 (*.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (*.f64 m (-.f64 1 m)) 1) v)) m) (*.f64 (neg.f64 1) m)): 7 points increase in error, 24 points decrease in error
    (+.f64 (*.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)) m) (*.f64 (neg.f64 1) m)): 0 points increase in error, 0 points decrease in error
    (+.f64 (*.f64 (Rewrite=> *-rgt-identity_binary64 (/.f64 (*.f64 m (-.f64 1 m)) v)) m) (*.f64 (neg.f64 1) m)): 0 points increase in error, 0 points decrease in error
    (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 m (/.f64 (*.f64 m (-.f64 1 m)) v))) (*.f64 (neg.f64 1) m)): 0 points increase in error, 0 points decrease in error
    (+.f64 (*.f64 m (/.f64 (*.f64 m (-.f64 1 m)) v)) (Rewrite=> *-commutative_binary64 (*.f64 m (neg.f64 1)))): 0 points increase in error, 0 points decrease in error
    (Rewrite<= distribute-lft-in_binary64 (*.f64 m (+.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (neg.f64 1)))): 5 points increase in error, 2 points decrease in error
    (*.f64 m (Rewrite<= sub-neg_binary64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))): 0 points increase in error, 0 points decrease in error
    (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)): 0 points increase in error, 0 points decrease in error

  3. Final simplification0.2

    \[\leadsto m \cdot \left(\frac{m}{v} \cdot \left(1 - m\right) + -1\right) \]

Reproduce

herbie shell --seed 2022334 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (and (< 0.0 m) (< 0.0 v)) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))